Spatiotemporal behavior in a predator–prey model with herd behavior and cross-diffusion and fear effect

Souna, Fethi; Djilali, Salih; Lakmeche, Abdelkader

doi:10.1140/epjp/s13360-021-01489-7

Cited by 34 publications

(6 citation statements)

References 53 publications

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“…In the past few years, mathematical models have become increasingly popular in studying how predation fear affects the growth rate of prey [14][15][16][17][18][19][20]. Křivan [21] investigated the trade-off between foraging and predation using the Lotka-Volterra model, which considers the adaptability of both the prey and predator to maximize their fitness.…”

Section: Introductionmentioning

confidence: 99%

Trade-off dynamics and chaotic behavior in nonautonomous prey-predator model with group defense

Bhargava,

Dubey

2023

Nonlinear Dyn

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Ecological "trade-off" is prioritising one trait over another. Predators put their lives at danger to pursue dangerous prey, and their injuries can reduce their chances of survival. Prey must "trade-off" between reproduction rate and safety, whereas predators must "trade-off" between food and safety. We present a two-dimensional prey and predator model that takes into account prey logistic growth rate and Monod-Haldane type functional response to reflect prey collective defense. We investigate the cost of fear in order to depict prey trade-off dynamics, and we change the predator's mortality rate by incorporating a function that reflects predator loss as a result of encountering dangerous prey. Our model shows bistability and goes through transcritical bifurcation, saddle node bifurcation, Hopf bifurcation, Bogdanov-Takens bifurcation, Bautin bifurcation, Homoclinic bifurcation, and Limit point of cycle bifurcation.We investigated the effects of our critical parameters on both populations and discovered that predators become extinct if their loss of predator is too high due to encounters with dangerous prey, demonstrating how predators risk their own health for food. We find that fear can lead to global stability in a system by causing the stable and unstable limit cycles to collide. We also see that the degree of seasonality in the level of fearin the nonautonomous model might lead to chaos. Sensitivity analysis, the positivity of the maximal Lyapunov exponent, and the uneven distribution of points observed in the Poincar map shown is an established sign of chaotic nature. We note that variations in intensity of seasonality in carry-over can cause a system to shift under many different periodic windows. The findings presented in this article may be beneficial in comprehending the biological insights derived from investigating prey-predator interactions..

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Section: Introductionmentioning

confidence: 99%

Trade-off dynamics and chaotic behavior in nonautonomous prey-predator model with group defense

Bhargava,

Dubey

2023

Nonlinear Dyn

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“…14,15 In the real world, the spatial distribution of population is inhomogeneous, so it is particularly important to consider the reaction-diffusion predator-prey model. [16][17][18][19] Spatial patterns and spatially inhomogeneous periodic solutions are important research contents, but the stable periodic solutions in numerical simulation are often spatially inhomogeneous. Based on the model (1.1), Yang et al considered the spatial diffusion and the competition in predator and showed the Hopf bifurcation induced by time delay.…”

Section: Introductionmentioning

confidence: 99%

“…In the real world, the spatial distribution of population is inhomogeneous, so it is particularly important to consider the reaction–diffusion predator–prey model 16–19 . Spatial patterns and spatially inhomogeneous periodic solutions are important research contents, but the stable periodic solutions in numerical simulation are often spatially inhomogeneous.…”

Section: Introductionmentioning

confidence: 99%

Spatially inhomogeneous bifurcating periodic solutions induced by nonlocal competition in a predator–prey system with additional food

Yang

Wang

Jin

2022

Math Methods in App Sciences

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The nonlocal competition in prey is incorporated into a diffusive predator-prey model with additional food in predator and time delay. The local stability of the coexisting equilibrium is studied by analyzing the eigenvalue spectrum. Time delay inducing Hopf bifurcation is also investigated by using time delay as bifurcation parameter. Some conditions for determining the bifurcation direction and the stability of the bifurcating periodic solutions are given by utilizing the normal form method and center manifold theorem. Our results suggest that nonlocal competition together with time delay can induce spatially inhomogeneous bifurcating periodic solutions in the diffusive predator-prey model.

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“…Wang and Zou [8] proposed a reaction-diffusion convective predator-prey model, which incorporated the fear effect into the local response term of the model. The authors of [9][10][11][12][13][14] studied the effect of the fear effect on the models from different aspects.…”

Section: Introductionmentioning

confidence: 99%

Steady states of a diffusive predator-prey model with prey-taxis and fear effect

Cao

Hao

2022

Bound Value Probl

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In this paper, a diffusive predator-prey system with a prey-taxis response subject to Neumann boundary conditions is considered. The stability, the Hopf bifurcation, the existence of nonconstant steady states, and the stability of the bifurcation solutions of the system are analyzed. It is proved that a high level of prey-taxis can stabilize the system, the stability of the positive equilibrium is changed when χ crosses $\chi _{0}$ χ 0 , and the Hopf bifurcation occurs for the small s. The system admits nonconstant positive solutions around $(\bar{u}, \bar{v}, \chi _{i} )$ ( u ¯ , v ¯ , χ i ) , the stability of bifurcating solutions are controlled by $\int _{\Omega} \Phi _{i}^{3} \,\mathrm{d}x$ ∫ Ω Φ i 3 d x and $\int _{\Omega} \Phi _{i}^{4} \,\mathrm{d}x$ ∫ Ω Φ i 4 d x . Finally, numerical simulation results are carried out to verify the theoretical findings.

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Spatiotemporal behavior in a predator–prey model with herd behavior and cross-diffusion and fear effect

Cited by 34 publications

References 53 publications

Trade-off dynamics and chaotic behavior in nonautonomous prey-predator model with group defense

Trade-off dynamics and chaotic behavior in nonautonomous prey-predator model with group defense

Spatially inhomogeneous bifurcating periodic solutions induced by nonlocal competition in a predator–prey system with additional food

Steady states of a diffusive predator-prey model with prey-taxis and fear effect

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